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Optimization and phenotype allocation

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Jost, Jürgen and Wang, Ying (2014) Optimization and phenotype allocation. Bulletin of Mathematical Biology, Volume 76 (Number 1). pp. 184-200. doi:10.1007/s11538-013-9915-5

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Official URL: http://dx.doi.org/10.1007/s11538-013-9915-5

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Abstract

We study the phenotype allocation problem for the stochastic evolution of a multitype population in a random environment. Our underlying model is a multitype Galton–Watson branching process in a random environment. In the multitype branching model, different types denote different phenotypes of offspring, and offspring distributions denote the allocation strategies. Two possible optimization targets are considered: the long-term growth rate of the population conditioned on nonextinction, and the extinction probability of the lineage. In a simple and biologically motivated case, we derive an explicit formula for the long-term growth rate using the random Perron–Frobenius theorem, and we give an approximation to the extinction probability by a method similar to that developed by Wilkinson. Then we obtain the optimal strategies that maximize the long-term growth rate or minimize the approximate extinction probability, respectively, in a numerical example. It turns out that different optimality criteria can lead to different strategies.

Item Type: Journal Article
Divisions: Faculty of Science > Centre for Systems Biology
Journal or Publication Title: Bulletin of Mathematical Biology
Publisher: Springer New York LLC
ISSN: 0092-8240
Official Date: 1 January 2014
Dates:
DateEvent
1 January 2014Published
Volume: Volume 76
Number: Number 1
Page Range: pp. 184-200
DOI: 10.1007/s11538-013-9915-5
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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